1. Field of the Invention
The present invention relates to a method and an apparatus for recording and reconstructing various images as holograms, and to a method and an apparatus for performing diverse kinds of spatial frequency filtering such as low-pass filtering, high-pass filtering, wavelet transform and matched filtering during the process of holographic recording and reconstruction.
2. Description of the Related Art
The so-called holographic memory is getting attention for its ability to rapidly record and reconstruct images in increments of pages, and to record plural pages of images in multiplexed fashion within the same volume of an optical storage medium thereby storing huge quantities of image data. As such, the holographic memory is sometimes referred to as a promising next-generation computer file memory.
The holographic memory is used not only to record and reconstruct images but also to execute spatial frequency filtering for such purposes as image analysis, image compression, image decomposition and image retrieval. Spatial frequency filtering is a technique that involves carrying out optical Fourier transform to acquire a two-dimensional spectrum of input images and getting the acquired spectrum changed by use of a spatial frequency filter. This is a typical parallel optical computing technique capable of performing diverse kinds of computation and thus considered an optical convolution.
Typical devices of spatial frequency filtering (abbreviated to "filtering" hereunder where appropriate) include low-pass filters, high-pass filters and band-pass filters.
Generally, low-frequency components in the spectrum of an image correspond to an approximate structure of the image while high-frequency components constitute edges and fine structures of the image. A low-pass filter allows only low-frequency components of the image spectrum to pass through while blocking high-frequency component noise. Conversely, a high-pass filter lets high-frequency components alone to pass in order to extract image edges and highlight fine structures of the image. A band-pass filter permits only a specific spatial frequency band to pass through in such applications as image compression and analysis.
Holographic technology affords spatial frequency filters complex amplitude characteristics that provide optical correlation. This makes it possible to perform pattern recognition and retrieval.
Usually, undulating complex amplitude distributions cannot be recorded directly. Only light intensity distributions can be directly measured, and photography merely records intensity distributions. In contrast, holography permits recording and reconstruction of complex amplitude distributions by introducing carrier components into the distributions.
A filter that takes advantage of the above characteristic of holography is what is known as the matched filter. In computing correlations between a reference image and input images, the matched filter checks to see whether a specific pattern exists in a two-dimensional image, and detects the location of such a pattern if it is found to exist.
More robust variations of the matched filter have been proposed to implement higher capabilities of recognition. These variations include a phase-only matched filter (J. L. Horner et al., APPLIED OPTICS Vol. 23, pp. 812-816 (1984)) and a wavelet matched filter (Y. Sheng et al., OPTICS LETTERS Vol. 18, pp. 299-301 (1993)).
The phase-only matched filter records only phase components of a Fourier transformed image of an input object and phase components of a Fourier transformed image of a reference object. In addition to its enhanced efficiency of light utilization, the phase-only matched filter has correlation values in a .delta. function through autocorrelation. This affords the phase-only matched filter a higher recognition capability than that of conventional matched filters.
Features of an image tend to concentrate on its contour portions. Taking advantage of this fact, the waveletmatched filter removes low-frequency components of the reference and input images through wavelet transform and computes correlations between the high-frequency components involved, thereby attaining a high recognition capability.
Conventional methods for holographic recording and reconstruction as well as for filtering are described below with reference to FIGS. 23 through 25.
For holographic recording, parallel light 1 is applied to an image 91 to yield object light 2 as shown in FIG. 23. The object light 2 is subjected to Fourier transform by a lens 92. Transformed object light 3 is applied to an optical storage medium 93 while plane wave reference light 5 is emitted simultaneously to the storage medium 93 to record a hologram therein.
For holographic reconstruction, as depicted in FIG. 24, the same reference light 5 as that in recording is emitted to the optical storage medium 93. In response, the stored hologram yields diffracted light 6A onto an optical path of object light. The diffracted light 6A is subjected to inverse Fourier transform by a lens 94. Transformed diffracted light 7A is sent to a photo detector 95 to form an image thereon.
The reconstructed image is filtered as follows: a filter 100 having a two-dimensional transmittance distribution is interposed between the optical storage medium 93 and the lens 94. The filter thus positioned extracts only desired spatial frequency components from a Fourier spectrum of the diffracted light 6A.
Illustratively, low-pass filtering is carried out by getting the filter 100 to let pass only the low-frequency spectrum components at a central position of the Fourier spectrum of the diffracted light 6A while blocking peripherally located high-frequency spectrum components. High-pass filtering is performed in a reverse fashion. That is, the low-frequency spectrum components at the central position are blocked and the filter 100 allows only the high-frequency spectrum components on the periphery to pass through.
For computation of correlations between images, parallel light 1 is applied to an image 96 to obtain object light 2a as shown in FIG. 25. The object light 2a is subjected to Fourier transform by a lens 97. Transformed object light 3a is used as retrieval light that is emitted in the manner shown in FIG. 23 to the optical storage medium 93 that contains the image 91 as a hologram. In turn, the stored hologram yields diffracted light 6B onto an optical path of reference light. The diffracted light 6B is subjected to inverse Fourier transform by a lens 98. Transformed diffracted light 7B is sent to a photo detector 99 to form an image thereon.
For the recording method of FIG. 23, it is assumed for the purpose of simplification that a wave number vector k of object light conforms to the wave number of reference light; and that the object light 2 before Fourier transform is expressed as Oexp(-ikr), the object light 3 after Fourier transform as oexp(-ik'r), and the reference light 5 as R(=R*). On that assumption, a hologram T held on the optical storage medium 93 is defined by the expression (1) below. In the expression (1) and subsequent expressions, .alpha. is used to signify proportion. EQU T.alpha..vertline.R+oexp(-ik'r).vertline..sup.2 =.vertline.R.vertline..sup.2 +.vertline.o.vertline..sup.2 +R*oexp(-ik'r)+R*oexp(-ik'r) (1)
For the reconstructing method of FIG. 24, the hologram T may be subjected to the same reference light R(=R*) as the reference light 5 in effect for recording. In that case, diffracted light is defined by the following expression: EQU RT.alpha.{R.vertline.R.vertline..sup.2 +R.vertline.o.vertline..sup.2 +RR*oexp(-ik'r) +RRo*exp(-ik'r)} (2)
Because the reference light R(=R*) is plane wave light and because the third term in the expression (2) above is diffracted onto the optical path of object light, reconstructed diffracted light I (i.e., diffracted light 6A) is defined as EQU I.alpha.oexp(-ik'r) (3)
When the reconstructed diffracted light I is subjected to inverse Fourier transform by the lens 94, object light Oexp(-ikr) is obtained as the diffracted light 7A.
Meanwhile, for the correlation computing method of FIG. 25, the hologram T may be subjected to the same object light oexp(-ik'r) as the object light in effect for recording. In that case, the diffracted light is defined by the following expression: EQU oexp(-ik'r)T .alpha.(oexp(-ik'r).vertline.R.vertline..sup.2 +oexp(-ik'r).vertline.o.vertline..sup.2 +oexp(-ik'r)R*oexp(-ik'r) +oexp(-ik'r)Ro*exp(ik'r) (4)
Because the fourth term in the expression (4) above is diffracted onto the optical path of reference light, the reconstructed diffracted light I (i.e., diffracted light 6B) is defined as EQU I.alpha.oo* (5)
When the reconstructed diffracted light I is subjected to inverse Fourier transform by the lens 98, autocorrelation value .smallcircle..star-solid..smallcircle.* of object light is obtained as the diffracted light 7B. In this case, EQU .smallcircle..star-solid..smallcircle.*=.sub.-.infin..sup. 28.intg.o(r')o*(r'-r)dr' (6)
where, .sub.-.infin..sup..infin. signifies integration from -.infin.to .infin..
Applying object light of a desired image 96 as the object light 3a yields values of cross correlation between the image 96 and the image 91 stored as the hologram T. This provides matched filtering.
FIG. 26A shows a recorded hologram of an image containing numerous alphabetic characters as object light. FIG. 26B depicts a case where alphabetic character K is applied as a retrieved image. In this case, as shown in FIG. 26C, an autocorrelation peak appears in the location of the alphabetic character K in the stored image. Because cross correlation values with respect to the other alphabetic characters are judged to be smaller than the autocorrelation value, the presence and location of retrieved image K are detected in the stored image.
The conventional filtering methods outlined above have some disadvantages. The filter 100 having a two-dimensional transmittance distribution allows certain frequency components of the Fourier spectrum of the diffracted light 6A to pass through while blocking the remaining frequency components. The blocked frequency components are lost on the downstream side of filter 100 and are not available for acquiring reconstructed images of other frequencies. In other words, where the filter 100 is used as a low-pass filter, the high-frequency spectrum components of the diffracted light 6A are lost on the downstream side of the filter 100. Conversely, where the filter 100 is used as a high-pass filter, the low-frequency spectrum components of the diffracted light 6A are lost on the downstream side of the filter 100.
If it is desired to carry out low-pass and high-pass filtering concurrently, it is required conventionally to split the diffracted light 6A into two light waves on two optical paths. A low-pass filter needs to be positioned on one of the optical paths and a high-pass filter on the other optical path, with an inverse Fourier transform lens 94 and a photo detector 95 furnished on each optical path. The arrangements can amount to a complicated and bulky reconstructing optical system.
The conventional matched filtering method described above is capable of distinguishing autocorrelation values from cross correlation values with relative ease in images such as those in FIGS. 26A through 26C containing numerous high-order spatial frequency components. On the other hand, where images present numerous low-order spatial frequency components as in FIG. 27A, most of the image spectrum frequency components coincide with one another illustratively for a circle, a square and a triangle despite their obvious differences in shape. In such a case, if the image of, say, the triangle in FIG. 27B is desired to be retrieved, the autocorrelation and cross correlation values are hard to distinguish as shown in FIG. 27C. This makes it difficult to retrieve the target image.
One way to circumvent the difficulty above has been proposed as follows: as depicted in FIGS. 28A and 28B, contours (high-frequency components) of images, i.e., portions where image features concentrate, are extracted beforehand so that correlations between the contour images are computed. This makes it relatively easy to distinguish autocorrelation values from cross correlation values.
For example, the contour portions are extracted by use of a computer, or by an optical high-pass filtering method as disclosed in Japanese Published Unexamined Patent Application No. Hei 4-306787.
The above schemes require extraction of contour portions, which constitutes a specific preliminary process for correlation computation. This threatens to forfeit the high-speed retrieval capability of holographic memory. Holographic memory is deemed viable only if it ensures high-speed transmission, high-speed retrieval and mass storage capacity.
The above-described phase-only matched filter conceived as a matched filter of enhanced recognition capability offers correlation images of high S/N ratios. However, the filter is deprived of amplitude data about stored images and thus incapable of reconstructing original images. Likewise, the wavelet matched filter mentioned above provides high S/N ratios but lacks low-frequency components of stored images and is incapable of reconstructing original images. These matched filters are effective in computing correlations but no longer function as part of holographic memory for storing or reconstructing data.